Bounding generalized relative entropies: Nonasymptotic quantum speed limits

Area of Science:

• Quantum Information Science
• Theoretical Physics
• Information Theory

Background:

• Information theory provides a framework for understanding quantum mechanics.
• Relative entropy quantifies distinguishability between quantum states and probability distributions.
• Relative entropy is crucial in metrology, quantum thermodynamics, communication, and information.

Purpose of the Study:

• To establish bounds on generalized relative entropies under quantum processes.
• To derive quantum speed limits using relative entropy bounds.
• To explore connections with thermodynamics, coherence, asymmetry, and single-shot information theory.

Main Methods:

• Analysis of general unitary quantum channels.
• Derivation of bounds for generalized relative entropies (Rényi and Tsallis).
• Application of bounds to establish quantum speed limits.

Main Results:

• Established bounds on generalized relative entropies for unitary channels.
• Derived a family of quantum speed limits derived from relative entropy.
• Identified potential links to thermodynamics, quantum coherence, and asymmetry.

Conclusions:

• The derived bounds offer insights into how relative entropy changes under quantum evolution.
• The new quantum speed limits provide a tool for quantifying the speed of quantum processes.
• The study highlights the interconnections between information-theoretic quantities and fundamental quantum phenomena.